The integral of 1- 3cos(2x) is straightforward. The integral of [itex]cos^3(2x)[/itex] can be done by writing it as [itex]cos^3(2x)= cos(2x)(1- sin^2(2x))[/itex] and using the substitution u= sin(2x). The integral of [itex]cos^2(2x)[/itex] can be done by using the trig identity [itex]cos^2(2x)= (1/2)(1+ cos(4x))[/itex].